Connections keep up just fine. It's the game itself. The tick rate is 20. That is how many times a second the game updates. The game is playing at 60fps. That means for every three frames one is actual data and the other two are interpolated. More interpolation means more delay and can lead to sync issues. On top of that is the lag comp(rewind time) and a smoothing code to make everything appear to be working well.
For PC games a FPS should have at least a 60 tick rate. 100+ is desirable. I believe that because of the P2P on the consoles the tick rate was kept low to minimize bandwidth. By tripling the tick rate to 60 you would also be tripling the bandwidth required. This is still a very small amount of bandwidth.
With dedicated servers there is no reason not to fix this. I've been playing on dedicated servers on the xbox BO2.